Renzoku: rules, tips and free puzzles online

Renzoku is a Latin square with dots. Fill the grid so each row and column holds 1 to N once. A dot between two cells means their digits are consecutive, and every consecutive pair has one. Play Renzoku online free here, on grids from 5×5 to 8×8.

The name is Japanese for “consecutive”. The dots tell you a lot, but the places without a dot usually tell you more.

The rules

• The grid is N×N (5×5 to 8×8 here). Each row and column contains every digit from 1 to N exactly once.
• A dot between two neighbouring cells means their digits differ by exactly 1.
• Every such pair is marked. Two neighbours with no dot between them are never consecutive.

How to start

Ends of the range

1 has only one consecutive partner, 2, and N has only N − 1. A 1 with a dot beside it settles that neighbour at once.

Use the missing dots

No dot between two cells means each rules out two digits from the other: if one is 4, the other is not 3 or 5. In a small grid, that leaves very few options.

Dots on both sides

A cell with dots to its left and right has one neighbour a step below and one a step above, so it can’t be 1 or N. Pairs and hidden singles in rows and columns finish the job, as in our solving techniques guide.

Common mistakes

• Ignoring the places without a dot. They are rules too.
• Thinking a dot means “one more”. It works in either direction: 5 and 4 are just as consecutive as 4 and 5.
• Forgetting that every row and column needs all of 1 to N.

How the ranks scale difficulty

The same four ranks apply here as everywhere on the site. Lemma is a gentle warm-up, Proposition needs a real idea or two, Theorem is near-minimal with almost every clue load-bearing, and Conjecture is the sparsest of all, so expect to think hard.

Grids run from 5×5 at Lemma to 8×8 at Conjecture, with very few given digits. The dots carry nearly all the information.

There are 99,999 puzzles per rank, each with its own number, so you can replay one or share it. Every type also has a 30-puzzle collection that climbs from Lemma to Conjecture. Every puzzle is checked to have exactly one solution that you can reach by logic alone, with no guessing.

Keep exploring

• FutoshikiA Latin square with < and > signs between neighbouring cells.
• Kropki SudokuWhite dots for consecutive pairs, black for a 1:2 ratio. Missing dots matter.
• Non-Consecutive SudokuSide-by-side cells never hold consecutive digits.
• Solving techniquesSingles, pairs, cage arithmetic, line logic and Latin squares, all in one guide.
• All puzzle guidesEvery puzzle type on Hoot’s Puzzles, with rules and tips.